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(B) $(1)$ False: For two triangles to be congruent by the $SAS$ (Side-Angle-Side) congruence rule,the angle must be included between the two sides. He

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False

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(B) $(1)$ False: For two triangles to be congruent by the $SAS$ (Side-Angle-Side) congruence rule,the angle must be included between the two sides. Here,in $\Delta ABC$,the angle between $AB$ and $BC$ is $\angle B$. In $\Delta PQR$,the angle between $PQ$ and $PR$ is $\angle P$. However,the given condition is $BC = PR$,but the sides forming $\angle P$ are $PQ$ and $PR$. Since $BC$ is not the side $QR$,the $SAS$ criterion is not satisfied.$(2)$ True: The sum of an interior angle and its corresponding exterior angle is $180^{\circ}$. If an exterior angle is acute $( 90^{\circ})$. $A$ triangle can have at most one obtuse angle. Therefore,it is impossible for two exterior angles to be acute,as that would imply the existence of two obtuse interior angles,which violates the angle sum property of a triangle.

State whether each of the following statements is true or false:
$(1)$ In $\Delta ABC$ and $\Delta PQR$,$AB = PQ$,$BC = PR$ and $\angle B = \angle P$,then $\Delta ABC \cong \Delta PQR$.
$(2)$ The exterior angles at two vertices of any triangle cannot both be acute.

Similar Questions

If $\triangle ABC \cong \triangle PQR$ and $\triangle ABC$ is not congruent to $\triangle RPQ$,then which of the following is not true?

In triangles $ABC$ and $DEF$,$AB = FD$ and $\angle A = \angle D$. The two triangles will be congruent by the $SAS$ axiom if:

Prove that in a triangle,other than an equilateral triangle,the angle opposite to the longest side is greater than $\frac{2}{3}$ of a right angle.

If $\Delta ABC \cong \Delta RPQ,$ then which side of $\Delta PQR$ is equal to side $AB$ of $\Delta ABC$?

$S$ is any point in the interior of $\triangle PQR$. Show that $SQ + SR < PQ + PR$.

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State whether each of the following statements is true or false:$(1)$ In $\Delta ABC$ and $\Delta PQR$,$AB = PQ$,$BC = PR$ and $\angle B = \angle P$,then $\Delta ABC \cong \Delta PQR$.$(2)$ The exterior angles at two vertices of any triangle cannot both be acute.